faulty amplifier

I just recently tried to install an spl 2000d gorilla series amp in my brother's car and I'm pretty sure the amp's faulty. It was a budget setup hence spl. The problem is when I connect power and ground without any other connections the led indicator turns on not very bright but at a dimmer level. The remote turn on lead seems to have no effect on the amp at all it doesn't turn it on nor off. The other thing that is strange that I've never encountered before is when I connect the rca's the led indicator turns on brightly indicating that the amplifier is on even though the car is off. If I leave the power and disconnect everything else when I connect the rca's back in it does the same showing that it's on. I've opened up the amplifier but I really don't know what to look for. Could it be faulty wiring? I just don't see how that could be an issue. If it was ground then it wouldn't turn on at all. I'm running 4 gauge wire.

Check your fuse, it's possible the fuse is blown but is still sending a small amount of power through the amp. Use a DMM and check for power at the amp.

if the amp led gets brighter when you plug in the rca then it would seem to me that you have a very bad ground connection. its either loose or it is not screwed to bare metal. it might even be on a piece of the car that isnt connected to the chassis. if you can, test the power wire at the amp with a volt meter and hook one test lead to a known ground and touch the other lead to the positive on the amp. it should read somewhere between 12 volts and 14 volts. now take the lead you had on the known good ground and take the same reading with that lead hooked to the amp ground. if it reads more than a few 10ths of a volt less then you probably need to rethink your ground.